A054664 Number of 4-ary Lyndon words of length n with trace 0 mod 4.

1, 1, 5, 14, 51, 165, 585, 2032, 7280, 26163, 95325, 349350, 1290555, 4792905, 17895679, 67106816, 252645135, 954429840, 3616814565, 13743869130, 52357696365, 199911109725, 764877654105, 2932030657200, 11258999068416

Offset: 1

Author

N. J. A. Sloane, Apr 18 2000

Keywords

• nonn
• easy

Comments

Also number of 4-ary Lyndon words of length n with trace 2 mod 4.

Links

• F. Ruskey, Number of q-ary Lyndon words with given trace mod q

Crossrefs

Cf. A000048, A051841, A046211, A046209, A054660, etc.

Programs

Mathematica

a[n_] := 1/(4 n) Sum[GCD[d, 4] MoebiusMu[d] 4^(n/d), {d, Divisors[n]}];
Array[a, 30] (* Andrey Zabolotskiy, Dec 19 2020 *)

Formula

From Andrey Zabolotskiy, Dec 19 2020: (Start)

a(n) = A068596(n) + A074403(n) + A074404(n) + A074405(n).

a(n) = A074410(n) + A074411(n) + A074412(n) + A074413(n). (End)

Extensions

More terms from James Sellers, Apr 19 2000